Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define inf (int)1e9
using namespace std;

int n, m, s, t;
vector<vector<int>> edge;
vector<int> ds, dt;
queue<int> qu;
map<int, long long> mps, mpt;

long long solve();

int main() {
  cin >> n >> m >> s >> t;
  --s, --t;
  edge.resize(n);
  for(int i = 0; i < m; ++i) {
    int x, y;
    cin >> x >> y;
    edge[--x].push_back(--y);
    edge[y].push_back(x);
  }
  cout << solve() << endl;
  return 0;
}

long long solve() {
  ds.assign(n, inf);
  dt.assign(n, inf);
  ds[s] = 0;
  dt[t] = 0;
  qu.push(s);
  while(!qu.empty()) {
    int now = qu.front();
    qu.pop();
    for(int i = 0; i < edge[now].size(); ++i)
      if(ds[edge[now][i]] == inf) {
        ds[edge[now][i]] = ds[now] + 1;
        qu.push(edge[now][i]);
      }
  }
  qu.push(t);
  while(!qu.empty()) {
    int now = qu.front();
    qu.pop();
    for(int i = 0; i < edge[now].size(); ++i)
      if(dt[edge[now][i]] == inf) {
        dt[edge[now][i]] = dt[now] + 1;
        qu.push(edge[now][i]);
      }
  }
  for(int i = 0; i < n; ++i) {
    ++mps[ds[i]];
    ++mpt[dt[i]];
  }
  long long ans = 0, target = ds[t] - 2;
  for(auto nmp : mps) {
    long long nowds = nmp.first, nowdt;
    nowdt = target - nowds;
    ans += nmp.second * mpt[nowdt];
  }
  return ans;
}